Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Royal Society University Research Fellow







614Huxley BuildingSouth Kensington Campus





Publication Type

5 results found

Feyzbakhsh S, Thomas RP, 2023, Rank r DT theory from rank 1, Journal of the American Mathematical Society, Vol: 36, Pages: 795-826, ISSN: 0894-0347

Fix a Calabi-Yau 3-fold X satisfying the Bogomolov-Gieseker conjecture ofBayer-Macr`ı-Toda, such as the quintic 3-fold.We express Joyce’s generalised DT invariants counting Gieseker semistable sheaves ofany rank r on X in terms of those counting sheaves of rank 1. By the MNOP conjecturethey are therefore determined by the Gromov-Witten invariants of X.

Journal article

Feyzbakhsh S, 2022, An effective restriction theorem via wall-crossing and Mercat's conjecture, MATHEMATISCHE ZEITSCHRIFT, Vol: 301, Pages: 4175-4199, ISSN: 0025-5874

Journal article

Feyzbakhsh S, Li C, 2021, Higher rank Clifford indices of curves on a K3 surface, SELECTA MATHEMATICA-NEW SERIES, Vol: 27, ISSN: 1022-1824

Journal article

Feyzbakhsh S, 2020, Mukai’s program (reconstructing a K3 surface from a curve) via wall-crossing, Journal für die reine und angewandte Mathematik, Vol: 2020, Pages: 101-137, ISSN: 0075-4102

Let C be a curve of genus g=11 or g≥13 on a K3 surface whose Picard group is generated by the curve class [C]. We use wall-crossing with respect to Bridgeland stability conditions to generalise Mukai’s program to this situation: we show how to reconstruct the K3 surface containing the curve C as a Fourier–Mukai transform of a Brill–Noether locus of vector bundles on C.

Journal article

Feyzbakhsh S, Thomas RP, 2019, An application of wall-crossing to Noether-Lefschetz loci, Publisher: arXiv

Consider a smooth projective 3-fold $X$ satisfying the Bogomolov-Giesekerconjecture of Bayer-Macr\`{i}-Toda (such as $\mathbb P^3$, the quinticthreefold or an abelian threefold). Let $L$ be a line bundle supported on a very positive surface in $X$. If$c_1(L)$ is a primitive cohomology class then we show it has very negativesquare.

Working paper

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